Superconformal Coset Equivalence from Level-Rank Duality

TL;DR

This paper establishes a precise correspondence between two N=2 superconformal coset models derived from Grassmannian cosets, demonstrating their equivalence through level-rank duality and preserved algebraic structures.

Contribution

It constructs an explicit one-to-one map between primary fields of the models and proves the invariance of key conformal data, confirming their equivalence.

Findings

Primary fields are in one-to-one correspondence

Conformal weights and charges are preserved

Fusion rules and modular matrices are invariant

Abstract

We construct a one-to-one map between the primary fields of the N=2 superconformal Kazama-Suzuki models G(m,n,k) and G(k,n,m) based on complex Grassmannian cosets, using level-rank duality of Wess-Zumino-Witten models. We then show that conformal weights, superconformal U(1) charges, modular transformation matrices, and fusion rules are preserved under this map, providing strong evidence for the equivalence of these coset models.